# ESA: Example Sieve Approach for Multi-Positive and Unlabeled Learning

arXiv: https://arxiv.org/abs/2412.02240 · HTML: https://mlsanity.com/paper/2412.02240/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 14 of 14)

- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [One-Class Classification: Taxonomy of Study and Review of Techniques](https://mlsanity.com/paper/1312.0049/) (2013)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Unbiased Risk Estimators Can Mislead: A Case Study of Learning with Complementary Labels](https://mlsanity.com/paper/2007.02235/) (2020)
- [Distantly Supervised Named Entity Recognition via Confidence-Based Multi-Class Positive and Unlabeled Learning](https://mlsanity.com/paper/2204.09589/) (2022)
- [Dropout Rademacher Complexity of Deep Neural Networks](https://mlsanity.com/paper/1402.3811/) (2014)
- [An Unbiased Risk Estimator for Learning with Augmented Classes](https://mlsanity.com/paper/1910.09388/) (2019)
- [Beyond Myopia: Learning from Positive and Unlabeled Data through Holistic Predictive Trends](https://mlsanity.com/paper/2310.04078/) (2023)
- [Robust Positive-Unlabeled Learning via Noise Negative Sample Self-correction](https://mlsanity.com/paper/2308.00279/) (2023)
- [Dens-PU: PU Learning with Density-Based Positive Labeled Augmentation](https://mlsanity.com/paper/2303.11848/) (2023)
- [A Positive-Unlabeled Metric Learning Framework for Document-Level Relation Extraction with Incomplete Labeling](https://mlsanity.com/paper/2306.14806/) (2023)
- [Positive-Unlabeled Node Classification with Structure-aware Graph Learning](https://mlsanity.com/paper/2310.13538/) (2023)

## Abstract (arXiv)

Learning from Multi-Positive and Unlabeled (MPU) data has gradually attracted significant attention from practical applications. Unfortunately, the risk of MPU also suffer from the shift of minimum risk, particularly when the models are very flexible as shown in Fig.refmoti. In this paper, to alleviate the shifting of minimum risk problem, we propose an Example Sieve Approach (ESA) to select examples for training a multi-class classifier. Specifically, we sieve out some examples by utilizing the Certain Loss (CL) value of each example in the training stage and analyze the consistency of the proposed risk estimator. Besides, we show that the estimation error of proposed ESA obtains the optimal parametric convergence rate. Extensive experiments on various real-world datasets show the proposed approach outperforms previous methods.